1. Technical Field
The present invention relates to a color gamut surface generating apparatus and a computer-readable medium storing a program that causes a computer to generate a color gamut surface.
2. Related Art
When color management is performed between output apparatuses for outputting color images, such as printing apparatuses and/or display apparatuses, it is necessary to fit given colors in a color gamut representing a color reproduction range of each output apparatus. A process of fitting colors in a color gamut, that is, a process of converting colors which cannot be reproduced into colors which can be reproduced is commonly called “color gamut mapping process”.
FIG. 14 is a conceptual view of the color gamut mapping process. FIG. 14 shows a color gamut in the LAB space, which is a standardized color space having no dependency on an output apparatus, where a color gamut of an output apparatus is indicated by a solid line, and a range of given colors (given color gamut) is indicated by a dashed line. Of colors in the color gamut indicated by the dashed line, colors which are outside of the color gamut indicated by the solid line cannot be reproduced by the output apparatus. Accordingly, as indicated by arrows in the figure, the colors shown outside of the color gamut indicated by the solid line are converted into colors belonging to the color gamut indicated by the solid line. Such a conversion process allows the color gamut indicated by the dashed line to be compressed (mapped) into the color gamut indicated by the solid line.
When such a color gamut mapping process is performed, it is first determined as to whether or not given colors can be reproduced in the output apparatus. Then, at least colors which cannot be reproduced are converted into colors which can be reproduced. Here, in order to determine whether or not the given colors can be reproduced in the output apparatus, a limit in color which can be reproduced in the output apparatus has to be acquired in advance, and it is necessary to quantify the surface (outline, contour) of the color gamut of the output apparatus.
FIGS. 15A and 15B are explanatory views of examples of a color gamut surface. For example, the color gamut surface of an output apparatus outputting a color image with the three colors of C (cyan), M (magenta) and Y (yellow) corresponds to the surface of a cube or a rectangular parallelepiped in a CMY color space as shown in FIG. 15A (in FIG. 15A, the surface of the cub has six sub-faces). A result of converting points on the surface of the cube or rectangular parallelepiped into the LAB color space is roughly shown in FIGS. 15A and 15B. In this case, since both the CMY color space as a conversion source and the LAB color space as a conversion destination are three-dimensional, one-to-one mapping can be performed. Accordingly, by converting points on the color gamut surface in the CMY color space into those in the LAB color space, the color gamut surface is expressed in the LAB without being changed its skeleton (primitive) although its shape is distorted. For example, if the conversion source is a different three-dimensional color space such as an RGB color space and if the conversion destination is also a three-dimensional color space, such a mapping relationship can be established. In addition, for example, if the output apparatus is a color printer, the conversion of colors in the CMY color space into those in the LAB color space may be performed in the following manner. That is, the color printer outputs color patches composed of combinations of C, M and Y, and then the color conversion is calculated based on a correspondence relationship between the combinations of C, M and Y and L*, a* and b* which are colorimetric values.
In this manner, when both color spaces of the conversion source and the conversion destination are three-dimensional, a color gamut surface is obtained according to the one-to-one mapping relation. However, if the color space of the conversion source is four-dimensional, for example, if the output apparatus uses K (black) in addition to C, M and N; conversion of a four-dimensional color space into a three-dimensional color space is performed. In this case, a many-to-one mapping relationship is mathematically established. Accordingly, the conversion using the one-to-one mapping shown in FIGS. 15A and 15B cannot be applied as it is.
JP 2003-8912 A and JP 2005-63093 A (corresponding to US 2005/0062992 A) describe methods of converting a color gamut surface in a four-dimensional color space such as CMYK color space into a three-dimensional color space such as LAB color space. FIG. 16 is an explanatory view of a method of obtaining a four-color gamut surface in LAB color space. In JP 2003-8912 A, a color gamut surface of three colors of CMY is first converted into the LAB color space as shown in FIG. 16. FIG. 16 shows sub-faces of a color gamut surface for tertiary colors which are obtained by using the three colors of CMY. Hatching is drawn in one sub-surface thereof. A color gamut surface for four colors is obtained by, for example, performing a dichotomizing search between points on the shown color gamut surface for the three colors and points out of a color gamut of CMYK. Accordingly, a color gamut surface for the case where four colors are used is obtained in the LAB color space.
FIG. 17 is an explanatory view of another method of obtaining a color gamut surface using four colors in the LAB color space. In JP 2005-63093 A, a color gamut surface is theoretically defined in CMYK color space. After points constituting a color gamut surface in the CMYK color space are obtained, a color gamut in LAB color space is obtained by converting the points (four dimension) on the color gamut surface into points (three dimension) in the LAB color space. The color gamut surface in the CMYK color space is defined by sub-faces shown in FIGS. 17A and 17B. In these figures, assuming that each component has a value between 0% and 100%, the characters “C”, “M”, “Y” and “K” in the figure indicate points of 100%, in the respective components. Also, when two or more symbols are combined, it represents 100% in the respective components. For example, CM stands for C=M=100%, MYK stands for M=Y=K=100%, and CMYK stands for C=M=Y=K=100%. By converting the sub-faces shown in FIGS. 17A and 17B into the LAB color space, a color gamut surface is obtained as shown in FIG. 17C. In addition, for example, if the output apparatus is a color printer, such conversion is calculated in the following manner. That is, the color printer outputs color patches composed of combinations of C, M, Y and K, and the conversion is calculated based on a correspondence relationship (color conversion model) between the combinations of C, M, Y and K and L*, a* and b*, which are colorimetric values.
Some output apparatuses may put a limitation on each color component or the sum of the color components. For example, a CMY color space may be converted into the LAB color space after the cube or rectangular parallelepiped shown in FIG. 15A is partially deleted and deformed according to the limitation. In this case, the order in which points are arranged in the CMY color space is preserved (maintained) in the LAB color space. When the shape of a color gamut in CMYK color space is controlled according to the limitation, it is determined as to whether or not the shape is established as a color gamut surface in LAB color space depending on how to define K. For example, in the case where there is a limitation of 280% on the total sum of CMYK as a limitation on the total sum of color components (hereinafter referred to as “total sum limitation”), C=M=Y=90% and K=30% do not meet the total sum limitation. However, C=M=Y=30% and K=90% meet the total sum limitation. Accordingly, how to define K determines whether or not a color gamut surface meets the total sum limitation in the LAB color space.
If some colors among the colors on the sub-faces shown in FIGS. 17A and 17B don't meet the total sum limitation, JP 2005-63093 obtains colors, meeting the total sum limitation, on the color gamut surface by fixing K or one color component having a larger value than the other components and decreasing the other components with their ratio being maintained.